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The topologist’s world map (2020)
- 082349872349872 4y agoI still find a Spilhaus projection more informative, but this is defo interesting!
- roter 4y agoDefinitely if you're an oceanographer. Interesting link here [0]. [0] https://storymaps.arcgis.com/stories/756bcae18d304a1eac140f19f4d5cb3d https://storymaps.arcgis.com/stories/756bcae18d304a1eac140f1...
- wnkrshm 4y agoThis is beautiful, especially with the colors on the top right - though I have a nitpick that it is missing an entire continent (probably because it doesn't show up in a list of countries): Antarctica Edit: I now realize it's only supposed to show the graph national borders, though on a political world map, Antarctica is still shown. In a topological fashion, it could be added as a white circle around the entire map.
- School-Cotton 4y agoAntarctica isn’t shown for the same reason the bottom of the ocean or the surface of the moon aren’t shown: there are no countries there. Adding cells that don’t correspond to a country (like your proposed white circle) would make the map less accurate.
- iso1631 4y agoThen you get onto the definition of what a country is - there are many countries claiming land in Antarctica.
- School-Cotton 4y agoIndeed, but those claims don’t really reflect any on-the-ground reality, and the majority of countries don’t recognize them.
- iso1631 4y agoThere are many disputed territories shown - Palestine (especially the bit bordering Jordan, which bares no relation to the facts on the ground), or Taiwan which is shown when only a dozen countries recognise it. Northern Cyprus which is defacto a different state to Mainland Cyprus isn't shown, but the UK military bases are shown. Gibraltar is erroneously shown as part of the UK, but the Falklands aren't shown at all -- nor are many other island territories. Hong Kong and Macau aren't shown as separate to China. It's difficult to know what the definition for inclusivity is.
- mths 4y ago> In a topological fashion, it could be added as a white circle around the entire map. You know the flat earthers would run wild with that map.
- wnkrshm 4y agoYou're right, better to invert it and put antarctica in the middle.
- hoseja 4y agoThat tiny Canada-Panama striped tail containing the entirety of North and Central America is funny.
- 082349872349872 4y agoThis map tends to give vertex-like countries large areas, and vice-versa.
- MonkeyClub 4y agoThe site is currently being hugged to death, so if you find its resources exhausted, try the archived version from a couple of hours back: http://web.archive.org/web/20221219173909/tafc.space/qna/the-topologists-world-map/ http://web.archive.org/web/20221219173909/tafc.space/qna/the...
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- ogogmad 4y agoFor people who have time to burn being uselessly pedantic, is this a topologist's world map up to homotopy equivalence or homeomorphism? [edit] I think I get how to encode a hypergraph as a topological space. Let S be a set consisting of two kinds of points: Nodes and hyperedges. Endow it with a topology whose base consists of singleton sets containing only single nodes, and sets containing a hyperedge together with all the nodes it's connected to. In particular, a hyperedge cannot be in an open set unless it's accompanied by the nodes it's connected to. Observations are: The resulting space is usually not T2 or T1, but is always T0; connectivity of the hypergraph is equivalent to connectivity of the topological space; the Sierpinski space results from using a graph with one node and edge. I don't know what that accomplishes except validate the intuition that graph theory is somehow connected to topology.
- ouid 4y agoHomotopy equivalence of what? This isnt really a topological space. It is a pair of spaces, one of which is contained in the other, (the sphere and the borders). This changes the category, morphisms are now pairs of morphisms and must preserve inclusion. The answer is neither, since there is no continuous map that increases the number of connected components of a space and there are more islands than show up on the map. There are other obstacles as well, alaska adds a piece to canada's boundary, this changes the fundamental group of the subspace, which is an invariant of homotopy type, and so the reduced version cannot be homotopy equivalent to the subspace with alaska's boundary included.
- richardhod 4y agoThis gets Ireland so wrong it is unbelievable. Firstly the British isles are treated differently from all the other islands on the map, and it's hard to tell that there's even a blue line separating it from the rest of Europe. Secondly, Ireland doesn't even have a blue line, which implies it is connected by land to Britain And thirdly, Wales and Scotland should really be acknowledged, and at the same time you might suggest Northern Ireland as well.
- tomtomtom777 4y agoIt seems correct to me. The map shows the country "United Kingdom of Great Britain and Northern Ireland" (UK) without separating its constituent countries. This is what most political world maps do. Ireland does border by land to the UK, at the border of Northern Ireland. This is shown with the black line. Also it borders to the UK and all of the world's ocean bordering countries which is shown through the surrounding blue.
- mannykannot 4y agoIt is a little inconsistent in that it shows the Bosporus dividing Turkey and even the Suez Canal dividing Egypt, but not the Irish Sea dividing the UK - though the first two are nominally continental boundaries.
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- pimlottc 4y agoPresumedly they are counting the land border between Ireland and Northern Ireland (as part of UK), but it’s confusing with the water boundary called out between UK and France.
- richardhod 4y agoWhereas I would call Northern Ireland an exclave colony, although in the current political status fittest part of the UK, much as Puerto Rico is part of the US, or the non-Russia Soviet States were part of the Soviet Union.
- forgotpwd16 4y agoThe no-text version looks like Gallifreyan writing.
- BenoitP 4y agoI wonder how it would look like if we considered France's borders with the Netherland (at Saint Martin) and Brazil (at French Guiana).
- Someone 4y agoIt has both as exclaves: the France-Netherlands border in the group of islands at bottom left (nitpick: technically not a border with the Netherlands because St Maarten nowadays is an independent country in the kingdom of the Netherlands), just above Cuba, and the Belize exclave at the top of Brazil, bordering Surinam.
- standardUser 4y agoThe Kingdom of the Netherlands is the parent nation state, despite St Maarten's designation as a "country". It's no more an independent state than Scotland (which is to say, not independent). (also sorry to be pedantic)
- Zobat 4y agoPlaces Iceland in America, but other than that really nice.
- lastofthemojito 4y agoThat's not wrong geologically: https://www.icelandtravel.is/attractions/bridge-between-continents/ https://www.icelandtravel.is/attractions/bridge-between-cont... Obviously not the cultural convention though.
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- _moof 4y agoIceland emerged (is still emerging?) from the rift between the North American and Eurasian plates. Roughly speaking everything west of Þingvellir is on the North American plate, everything east on the Eurasian. I would've given it two colors in the continent map, although now that I look at it again it the categories seem to be more cultural than geologic, which would place it squarely in Europe.
- ecommerceguy 4y agoJust think if the Diomede islands were uplifted somehow, poof Russia and the USA have a border.
- thriftwy 4y agoIn winter there kind of is - I think you can walk by ice sometimes.
- lastofthemojito 4y agoBut don't expect a warm welcome if you make the trip: https://www.nbcnews.com/id/wbna12152629 https://www.nbcnews.com/id/wbna12152629
- todorstoyanov 4y agoFascinating how protected by their geography are USA, Canada, Ireland and maybe UK. The remaining countries have too many neighbors and, accordingly, potential opponents. Look at the Balkans or part of Africa. I live in Sofia, Bulgaria and it has always seemed silly to me that the reason our city was chosen as the capital was the fact that it is surrounded by mountains on all sides. Now with this war in Ukraine, this idea seems genius to me.
- malwrar 4y agoI wouldn't draw too strong of conclusions from this map. It does show relative proximity to things like oceans but doesn't show lakes, rivers, mountains (as you note), jungles, and other natural features that, from a geopolitical standpoint, have created and prevented conflict throughout history.
- anonporridge 4y agoThe geography of the USA, bordered by massive oceans and weak/friendly neighbors along with being a huge and productive landmass with a unified culture, is one of the many reasons why it is unbelievably overpowered as a country, and unlikely to lose its dominance anytime soon. China might be competitive in terms of massive, productive landmass, but it simply will never be as secure in its borders as the US with strong and less friendly neighbors all around it. That will hold it back from surpassing the US as the dominant superpower. Ditto India, Russia, Brazil, and any potential rising powers in Africa. By far, the biggest threat to US dominance is balkanization. Fracturing the union and creating deeper geographic divides in American culture would create enough internal strife to hamstring its power. Maybe that's inevitable over time for such a large landmass and the unique conditions of American colonization were never going to last more than a couple hundred years before it started falling apart.
- School-Cotton 4y agoWhy exactly does having strong rivals on your borders make you any less likely to become a superpower? Is your argument that before China gets strong enough to be considered a superpower, their neighbors will invade them? Or is that they’ll feel insecure about their borders, and allocate resources to their military rather than economic development? Both arguments seem far-fetched. War with one’s neighbors is never guaranteed, even though there’s a risk of it. And they’d have to spend an unrealistically huge portion of their gdp on border defense for that to make development impossible.
- HPsquared 4y agoCould be a nice basis for a board game.
- pjmorris 4y agoTopographical Risk!
- glitcher 4y agoI like how the Panama Canal is represented by the gap in the name Pan|ama. Nice work overall!
- hammock 4y agoIs there a mathematical reason why, on the US map, only three types of lines are needed to generate this map- vertical, horizontal and one diagonal? Does that notion generalize to all border maps and if so why? Is it related how border maps can all be colored with only four colors?
- trynewideas 4y ago> Is there a mathematical reason why No. Here's another topological map of the contiguous US that's all rectangles, arranged in a triangle: https://www.reddit.com/r/MapPorn/comments/gy2jq6/the_topologists_map_of_the_contiguous_united/ https://www.reddit.com/r/MapPorn/comments/gy2jq6/the_topolog... I'm not sure how much I'd overthink this map, since it appears to have been created as a puzzle for children to help them understand the concept of topology: https://www.1001mathproblems.com/2015_11_01_archive.html https://www.1001mathproblems.com/2015_11_01_archive.html > Does that notion generalize to all border maps and if so why? No. > Is it related how border maps can all be colored with only four colors? If you're talking about the four color map theorem? Instinctively, my answer's no, but it might be a fun thing to prove.
- madcaptenor 4y agoFor more maps like this, there are a bunch of quizzes on Sporcle that ask you to label the nodes of a graph, where the nodes are states/provinces/countries and the edges are borders: https://www.sporcle.com/playlists/Alcas/graph-y-geography https://www.sporcle.com/playlists/Alcas/graph-y-geography
- Someone 4y agoI would think horizontal and vertical line segments (or, by extension, straight line segments with two different orientations; take the map with only horizontal and vertical line segments and apply a shear mapping (https://en.wikipedia.org/wiki/Shear_mapping https://en.wikipedia.org/wiki/Shear_mapping) and a rotation) are sufficient. That’s basically what this is, if you draw it on a pixel grid.
- klyrs 4y ago
- twic 4y ago> It was at some point while I was thinking about adding extra countries to represent seas that it was time to call the automation quits, and just make the map manually. This has some advantages – I get to choose the overall layout, it’s much easier to include stylistic elements, and I don’t have to spend ages describing to a computer what common sense is. An all too familiar situation.
- sylogizmo 4y ago508'd, so I guess the comments will make sense tomorrow.
- TchoBeer 4y agoWhat's going on by Israel-Egypt
- hydrogen7800 4y agoEgyptian territory on both sides of the Suez canal.
- glxxyz 4y agoPrior art: https://upload.wikimedia.org/wikipedia/commons/4/48/Hereford-Karte.jpg https://upload.wikimedia.org/wikipedia/commons/4/48/Hereford...
- joshlemer 4y agoCanada actually now has a land border with Denmark! https://en.wikipedia.org/wiki/Hans_Island https://en.wikipedia.org/wiki/Hans_Island
- abbusfoflouotne 4y ago> It was at some point while I was thinking about adding extra countries to represent seas that it was time to call the automation quits, and just make the map manually. This has some advantages – I get to choose the overall layout, it’s much easier to include stylistic elements, and I don’t have to spend ages describing to a computer what common sense is. Though this is casually thrown out by the author and empathetically chuckled at by most of us, I this points to a problem worth exploring. In the wake of the hype around recent AI advancements, we can often view computers and software as capable of anything. But often the limits of our current computing systems are made glaringly obvious, such as stylistic design and a "common sense" disconnect articulated here. An area worth our attention and a domain possessing potential for innovation.
- culi 4y agoWhile I generally agree with this sentiment, I don't know if this is a good example. This doesn't really seem like an impossible problem to me so much as a really complicated one. Something that could likely be solved algorithmically without even the use of AI. Perhaps it could take information like the size and/or population of different countries to make best guesses on how large to make different parts of it. Even if it produces a best guess that you can then clean up in Inkscape it'd be a tremendous contribution to this task
- ISL 4y agohttps://web.archive.org/web/20221219173909/https://tafc.space/qna/the-topologists-world-map/ https://web.archive.org/web/20221219173909/https://tafc.spac...